## What is/are Three Dimensional Space?

Three Dimensional Space - To reconstruct the points in three dimensional space, we need at least two images.^{[1]}Firstly, the nonlinear measurement equations are pseudo-linearized and then an unbiased least squared estimator for target location in three dimensional space is derived, by which detector’s bearings-only measurements can be converted to target’s spatial position in Cartesian coordinates, and so the above-mentioned nonlinearity is improved greatly.

^{[2]}Therefore the assistive robot should be capable of analyzing and understanding numerical meaning of uncertain terms for the purpose of creating conceptual map for effective navigation in three dimensional space.

^{[3]}We consider all degrees of freedom in three dimensional space SE(3) and in the robot’s joint space Q.

^{[4]}In cutting simulation we use voxel as a unit of image in three dimensional space, and combine with the adaptive octree to reduce memory usage and the number of triangle meshes.

^{[5]}However, curve fitting with confined error in three dimensional space is nontrivial since the Hausdorff distance between a space G01 segment and a rational parametric curve segment is difficult to formulate.

^{[6]}The multiple UUVs move in three dimensional space.

^{[7]}In this case the drives are translated in the shaking tables DOFs in the three dimensional space.

^{[8]}The factor scores were scattered in a three dimensional space on activity, harmony, and potency axes.

^{[9]}Typical applications include source localization in two or three dimensional space,molecular conformation in three dimensions, graph embedding and data visualization.

^{[10]}Particularly for a positive rate of chemical growth, we prove the existence of a heteroclinic orbit by constructing a positively invariant set in the three dimensional space.

^{[11]}We propose a bosonic $U(1)$ rotor model on a three dimensional space-time lattice.

^{[12]}Instead of using a traditional four axis remote controller to steer the small sized quadrotors used in this work, all degrees of freedom of the device are intuitively controlled by a human operator in virtual reality, allowing high precision maneuvering of the vehicles through obstacles in three dimensional space.

^{[13]}The outer (position) loop of the control system implements small disturbance linearization of the roll and pitch attitude variables together with a Proportional-Derivative constrained control type of the position errors in the three dimensional space, and it provides attitude commands to the inner (attitude) loop for tracking the Quadrotor’ s center of gravity position coordinates in the instantaneous horizontal planes, in addition to the required thrust force.

^{[14]}Existing recommendation algorithms transform the three dimensional space of user, resource, and tag into two dimensions using pair relations in order to apply existing techniques.

^{[15]}By normalizing the three parameters, these channels can be turned into points in the three dimensional space, the point with smallest distance sum respected to all the other points can be chosen as the reference channel, the calibration time is reduced consequently.

^{[16]}Through coordinate transformation approach, crystal orientation dependences of magnetic properties have been investigated in the three dimensional space for bismuth ferrite (BiFeO3).

^{[17]}As the arm can move on three dimensional spaces, target purposes.

^{[18]}Finally, the effectiveness of the proposed method is illustrated through simulations in both two and three dimensional spaces.

^{[19]}The occurrence of variants with thematic or mythological significance and their clustering within the three dimensional space of the burial chamber are then evaluated as evidence for the use of master document(s), which have otherwise been lost, in the execution of the monument’s decorative program.

^{[20]}This article studies 3D formation building in three dimensional spaces by a team of mobile robotic sensors.

^{[21]}In this letter, we seek to maximize the amount of UAV-assisted data dissemination among spatially dispersed IoT devices by jointly optimizing the resource assignment strategy and UAV’s mobility in the three dimensional space.

^{[22]}In this paper we consider the complete state estimation problem of a vehicle navigating in a three dimensional space.

^{[23]}Two control methods are applied for the selected topology; Three Dimensional Space Vector Pulse Width Modulation (3D-SVPWM), Hysteresis.

^{[24]}The simulation results showed that the traditional ant colony algorithm and improved ant colony algorithm both could search out a security optimal path for rescuing & coal exploring robot in three dimensional space environment.

^{[25]}With significant technological improvements on earth observation instruments, three dimensional space-borne remote sensing data became indispensable for modelling large areas and continents.

^{[26]}The LES is conducted with the extending fifth-order positivity-preserving WENO scheme and great efforts are spent to reproduce the real flow situation by adopting the three dimensional space-developing method with detailed chemical reaction mechanism.

^{[27]}Motivated by the conduction properties of graphene discovered and studied in the last decades, we consider the quantum dynamics of a massless, charged, spin 1/2 relativistic particle in three dimensional space-time, in the presence of an electrostatic field in various configurations such as step or barrier potentials and generalizations of them.

^{[28]}Vectorcardiogram (VCG) is a recurring, near-periodic pattern of cardiac dynamics that graphically represents the trajectory of the tip of cardiac vectors in three dimensional space with varying time.

^{[29]}In this paper, we propose a weak Galerkin finite element method (WG) for solving the stationary incompressible Stokes equation in two or three dimensional space.

^{[30]}Due to the contact force the rod undergoes (large) bending deflections in three dimensional space which are described using a non-linear bending theory.

^{[31]}Three dimensional space provides a significant barrier to efficient and complete virus spread within tumors and needs to be explicitly taken into account for virus optimization to achieve the desired outcome of therapy.

^{[32]}Specifically, we propose an agent-based model of cell clones, a strategy for propagating information from our in silico cell clones to the tissue scale, and an analytical solution backed by numerical results to understand how differential growth between the cerebellar layers drives geometric instability in three dimensional space on the tissue scale.

^{[33]}We present algorithms for reconstructing, up to unavoidable projective automorphisms, surfaces with ordinary singularities in three dimensional space starting from their silhouette, or "apparent contour" - namely the branching locus of a projection on the plane - and the projection of their singular locus.

^{[34]}In particular, we consider algebras appearing as asymptotic symmetries of three dimensional spacetimes, the bms3$$ \mathfrak{b}\mathfrak{m}{\mathfrak{s}}_3 $$, u1$$ \mathfrak{u}(1) $$ Kac-Moody and Virasoro algebras.

^{[35]}Vectorcardiogram (VCG) represents the trajectory of the tip of cardiac vectors in three dimensional space with varying time.

^{[36]}Based on the continuity of the time since childhood, we classified the experiences and social relations according to the change of place in North Korea and South Korea chronologically, referring to the process of differentiation of critical events in the three dimensional space revealed in the interview process, The categorized experiences were categorized, interpreted, and verified for mainstreaming and sub-topics such as cultural adaptation, academic adjustment, career decision, and psychological characteristics.

^{[37]}The experiments span a three dimensional space with the base factors of concentration, pressure and temperature.

^{[38]}Of particular importance, guidance of the procedures required orientation in three dimensional space, information generally supplied by echocardiography, and accurate measurements of cardiac and great vessel size by CT or CMR.

^{[39]}In chapter 3, we extend the argument developed in chapter 2 to elastic surface grating problem, where the surface is assumed to be periodic and elastic rigid; Then, we treat the obstacle scattering in three dimensional space; The direct problem is shown to have a unique weak solution by examining its variational formulation.

^{[40]}The 3 D - LR criterion combines three of the most important attributes – prediction, separability, complexity – of each candidate model and map them into a three dimensional space to select the best one.

^{[41]}The alignment becomes tighter with cosmic time; the major axes of the CGs and their host DM haloes at present are aligned on average within $\sim 30^{\circ}$ in the three dimensional space and $\sim 20^{\circ}$ in the projected plane.

^{[42]}The Three Dimensional Space Vector Pulse Width Modulation (3D-SVPWM) is considered an effective tool for dealing with the unbalanced system rather than the Two Dimensional Space Vector Pulse Width Modulation 2D-SVPWM.

^{[43]}In this paper, we consider a group of double integrator systems in three dimensional space and study the modulus consensus problem problem with desired orientation.

^{[44]}In three dimensional space, null and X-points are shown to have analogous effects on magnetic reconnection.

^{[45]}First, a shape sensor using three fibers provides the position and orientation of joints in three dimensional space.

^{[46]}These symmetries are studied on a three dimensional space-like hypersurface Σ embedded in a four-dimensional space–time manifold.

^{[47]}In the numerical experiments, a realistic hydrocarbon component (isobutane) in three dimensional space is simulated by the proposed MRT-LB model.

^{[48]}

## two dimensional space

With the extension of acquisition time, the corresponding frequency first decreases and then becomes stable; the extracted liquor characteristic signal is projected into two-dimensional space and three-dimensional space.^{[1]}In this article, it is first mathematically proven that the “distance between points on any two different circles in three-dimensional space” is equivalent to the “distance of points on a vector ellipse from another fixed or moving point, as in two-dimensional space.

^{[2]}ABSTRACT The actual flying environment of quadrotor unmanned aircraft vehicle (UAV) is three-dimensional space, so this paper extends the traditional artificial potential field (APF) method from two-dimensional space to three dimensional space.

^{[3]}The approach is an extension of the pixel (2D raster cell) density around a point in two-dimensional space to the voxel density around a trajectory line segment in three-dimensional space-time $(x-y+t)$.

^{[4]}The system uses the built-in toolbox of MATLAB to complete the binocular camera calibration, use OpenCV to extract the corner information and edge information of the target, and use the SIFT stereo matching algorithm to stereo match the left and right image pairs, and then obtain the disparity map by writing the ranging program, reproject the two-dimensional space points into the three-dimensional space, realize the conversion from two-dimensional coordinates to three-dimensional coordinates, so as to obtain the distance between the mobile robot and the target in real time.

^{[5]}With the continuous development of computer science and technology, symbol recognition systems may be converted from two-dimensional space to three-dimensional space.

^{[6]}Results Three types of spaces are identified and presented metapsychologically: three-dimensional space (3D) constructed by the ego; the two-dimensional space (2D) that manifests itself to the Subject, in particular in the repetitive emergence of traumatic scenes; finally, an artistic experience (both creation and reception) that needs to be thought through topologically, and therefore in four dimensions (4D).

^{[7]}

## subcellular structures cell

Specifically, ClusterMap precisely clusters RNAs into subcellular structures, cell bodies, and tissue regions in both two- and three-dimensional space, and consistently performs on diverse tissue types, including mouse brain, placenta, gut, and human cardiac organoids.^{[1]}Specifically, ClusterMap precisely clusters RNAs into subcellular structures, cell bodies, and tissue regions in both two- and three-dimensional space, and consistently performs on diverse tissue types, including mouse brain, placenta, gut, and human cardiac organoids.

^{[2]}Specifically, ClusterMap precisely clusters RNAs into subcellular structures, cell bodies, and tissue regions in both two- and three-dimensional space, and performs consistently on diverse tissue types, including mouse brain, placenta, gut, and human cardiac organoids.

^{[3]}

## generalized taxicab distance

In this paper, we define the generalized taxicab distance function in three dimensional space, which includes the taxicab distance function as a special case, and we show that three dimensional generalized taxicab distance function determines a metric.^{[1]}In this paper, we first determine the generalized taxicab distance formulae between a point and a line and two parallel lines in the real plane, then we determine the generalized taxicab distance formulae between a point and a plane, two parallel planes, a point and a line, two parallel lines and two skew lines in three dimensional space, giving also the relations between these formulae and their well-known Euclidean analogs.

^{[2]}

## one dimensional time

Matter, Yin matter and etheric each have three-dimensional space coordinates, matter and Yin matter share a one-dimensional time coordinate, and etheric has an independent one-dimensional time coordinate, which constitutes the 11-dimensional space-time of the universe.^{[1]}I suggest taking time dimension more into consideration, and exploring a new direction on the research of DM and DE as typical relic of BM, positive mass made negative through a continuous phase transition, from a three-dimensional space dimension to the one-dimensional time.

^{[2]}

## Whole Three Dimensional Space

We study the conditional regularity for the incompressible Navier–Stokes equations in the whole three dimensional space in terms of one component of the velocity field u = ( u 1 , u 2 , u 3 ).^{[1]}Several intruder size and speed values are considered together with trajectories covering the whole three dimensional space.

^{[2]}

## three dimensional space vector

Two control methods are applied for the selected topology; Three Dimensional Space Vector Pulse Width Modulation (3D-SVPWM), Hysteresis.^{[1]}The Three Dimensional Space Vector Pulse Width Modulation (3D-SVPWM) is considered an effective tool for dealing with the unbalanced system rather than the Two Dimensional Space Vector Pulse Width Modulation 2D-SVPWM.

^{[2]}